Probability that life arose by random chance.

By ruling out that the existence of a creator and thus intelligent design how do reason with the probability that life arose from random chance?
Atheist Answer: 

View this excellent video for the leading chemical theory of abiogenesis, or the origin of life:

If you prefer not to get into the details, simply consider that
1. it's a 4.5 billion year old planet with a surface area of about half a billion square kilometres, and
2. it's a fact of evolution that all living things have a single common ancestor. (The ubiquity of DNA is the most obvious evidence of this.)

This means that the process of abiogenesis, however it happened and however unlikely, only had to happen once, and there was a vast amount of time and space to do it in. However small the chances of the particular process occurring in any given time and place, it had a practically infinite number of opportunities.

A similar situation is a lottery. The chances of winning it might be one in 50 million, but imagine if 50 million people each buy a ticket. There's still a chance that nobody will win (with these numbers, 36.79%), but the number of EXPECTED winners is exactly one. So if someone in another city wins it, nobody is surprised.

Don't underestimate random chance if the chances are good. It's only by random chance that you weren't hit by a meteorite today, or any other day.

- SmartLX

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